A line passes through the points (3, 10) and (7, 24). a. Find the slope of the line. b. Find an equation for the line .

ingerentayQL

ingerentayQL

Answered question

2022-11-27

A line passes through the points ( 3 , 10 )and ( 7 , 24 ).
a. Find the slope of the line.
b. Find an equation for the line .

Answer & Explanation

skilningugdK

skilningugdK

Beginner2022-11-28Added 15 answers

Given that a line passes through the points ( 3 , 10 ) and ( 7 , 24 ). Let f(n) be the function for the line. Then f ( 3 ) = 10 and f ( 7 ) = 24.
We are aware that the graph of a linear function is a line with a slope equal to the constant difference in the table. We can calculate the slope of that line by finding the slope between any two points on the line.
Therefore we can calculate the slope as change in output change in input
a) Thus slope of the line is f ( 7 ) f ( 3 ) 7 3 = 24 10 4 = 14 4
Thus slope = 7 2
The line equation will be the linear function that fits the points given. Let y = a x + b be the linear function.
Now for point ( 3 , 10 ), we get 10 = 3 a + b . . . .(1)
and for point ( 7 , 24 )), we get 24 = 7 a + b . . . . .(2)
Subtracting (1) from (2), we get
14=4a. Thus a = 7 2
Substituting the value of a from above in (1), we get
10 = 3 ( 7 2 ) + b
So, b = 10 21 2 = 1 2
Thus the the line equation will be y = 7 2 x 1 2 which can be further be written as 7 x 2 y 1 = 0

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